MinT - Best Known (30, 30+37, s)-Nets in Base 81

Best Known (30, 30+37, s)-Nets in Base 81

(30, 30+37, 370)-Net over F₈₁ — Constructive and digital

Digital (30, 67, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 67, 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]

(30, 30+37, 654)-Net over F₈₁ — Digital

Digital (30, 67, 654)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(30, 30+37, 939321)-Net in Base 81 — Upper bound on s

There is no (30, 67, 939322)-net in base 81, because

1 times m-reduction [i] would yield (30, 66, 939322)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 912036 567393 368235 750217 741861 160294 066321 436837 964829 911872 799901 898878 294074 267488 695725 169658 919413 327019 372115 618982 569281 > 81⁶⁶ [i]