MinT - Best Known (35, 107, s)-Nets in Base 27

Best Known (35, 107, s)-Nets in Base 27

(35, 107, 114)-Net over F₂₇ — Constructive and digital

Digital (35, 107, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 107, 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]

(35, 107, 172)-Net in Base 27 — Constructive

(35, 107, 172)-net in base 27, using

t-expansion [i] based on (34, 107, 172)-net in base 27, using
- 1 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]

(35, 107, 220)-Net over F₂₇ — Digital

Digital (35, 107, 220)-net over F₂₇, using

t-expansion [i] based on digital (33, 107, 220)-net over F₂₇, using
- net from sequence [i] based on digital (33, 219)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 33 and N(F) ≥ 220, using
    - Drinfeld modules of rank 1 [i]

(35, 107, 226)-Net in Base 27

(35, 107, 226)-net in base 27, using

1 times m-reduction [i] based on (35, 108, 226)-net in base 27, using
- base change [i] based on digital (8, 81, 226)-net over F₈₁, using
  - net from sequence [i] based on digital (8, 225)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 8 and N(F) ≥ 226, using
      - a curve from the manYPoints database [i]

(35, 107, 9846)-Net in Base 27 — Upper bound on s

There is no (35, 107, 9847)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1436 778511 276101 485970 452039 350931 197697 045000 337592 880322 562443 081681 854875 351010 930899 411539 753999 959256 595311 215330 255044 760826 433698 643780 184364 779225 > 27¹⁰⁷ [i]