MinT - Best Known (40, 88, s)-Nets in Base 27

Best Known (40, 88, s)-Nets in Base 27

(40, 88, 170)-Net over F₂₇ — Constructive and digital

Digital (40, 88, 170)-net over F₂₇, using

(u,Â u+v)-construction [i] based on
1. digital (7, 31, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]
2. digital (9, 57, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(40, 88, 334)-Net over F₂₇ — Digital

Digital (40, 88, 334)-net over F₂₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 88, 370)-Net in Base 27 — Constructive

(40, 88, 370)-net in base 27, using

8 times m-reduction [i] based on (40, 96, 370)-net in base 27, using
- base change [i] based on digital (16, 72, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(40, 88, 66779)-Net in Base 27 — Upper bound on s

There is no (40, 88, 66780)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 912236 351944 156118 537981 346516 515909 511062 519278 805642 412262 063396 288692 042007 107829 630115 326507 719775 925162 891895 994930 026561 > 27⁸⁸ [i]