MinT - Best Known (103−65, 103, s)-Nets in Base 27

Best Known (103−65, 103, s)-Nets in Base 27

(103−65, 103, 114)-Net over F₂₇ — Constructive and digital

Digital (38, 103, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 103, 114)-net over F₂₇, using
- net from sequence [i] based on digital (23, 113)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 23 and N(F) ≥ 114, using
    - an explicitly constructive algebraic function field [i]

(103−65, 103, 172)-Net in Base 27 — Constructive

(38, 103, 172)-net in base 27, using

t-expansion [i] based on (34, 103, 172)-net in base 27, using
- 5 times m-reduction [i] based on (34, 108, 172)-net in base 27, using
  - base change [i] based on digital (7, 81, 172)-net over F₈₁, using
    - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
        a function field by SÃ©mirat [i]

(103−65, 103, 244)-Net over F₂₇ — Digital

Digital (38, 103, 244)-net over F₂₇, using

t-expansion [i] based on digital (36, 103, 244)-net over F₂₇, using
- net from sequence [i] based on digital (36, 243)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 36 and N(F) ≥ 244, using
    - Drinfeld modules of rank 1 [i]

(103−65, 103, 298)-Net in Base 27

(38, 103, 298)-net in base 27, using

1 times m-reduction [i] based on (38, 104, 298)-net in base 27, using
- base change [i] based on digital (12, 78, 298)-net over F₈₁, using
  - net from sequence [i] based on digital (12, 297)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 12 and N(F) ≥ 298, using
      - a curve from the manYPoints database [i]

(103−65, 103, 17946)-Net in Base 27 — Upper bound on s

There is no (38, 103, 17947)-net in base 27, because

1 times m-reduction [i] would yield (38, 102, 17947)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 99 922179 555339 605487 452033 982314 118731 610417 781119 110462 793442 924159 995962 495256 278777 961519 426787 524289 482864 257901 805594 022689 147861 103966 434497 > 27¹⁰² [i]