MinT - Best Known (38, 38+66, s)-Nets in Base 27

Best Known (38, 38+66, s)-Nets in Base 27

(38, 38+66, 114)-Net over F₂₇ — Constructive and digital

Digital (38, 104, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 104, 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]

(38, 38+66, 172)-Net in Base 27 — Constructive

(38, 104, 172)-net in base 27, using

t-expansion [i] based on (34, 104, 172)-net in base 27, using
- 4 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]

(38, 38+66, 244)-Net over F₂₇ — Digital

Digital (38, 104, 244)-net over F₂₇, using

t-expansion [i] based on digital (36, 104, 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]

(38, 38+66, 298)-Net in Base 27

(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]

(38, 38+66, 16401)-Net in Base 27 — Upper bound on s

There is no (38, 104, 16402)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 72795 991037 057500 088008 593387 958445 762010 028288 971717 739864 410563 019029 299958 582381 175202 562321 045554 743190 859521 607365 634706 274178 465615 570577 634965 > 27¹⁰⁴ [i]