MinT - Best Known (33, 33+37, s)-Nets in Base 81

Best Known (33, 33+37, s)-Nets in Base 81

(33, 33+37, 370)-Net over F₈₁ — Constructive and digital

Digital (33, 70, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 70, 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]

(33, 33+37, 936)-Net over F₈₁ — Digital

Digital (33, 70, 936)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(33, 33+37, 1953877)-Net in Base 81 — Upper bound on s

There is no (33, 70, 1953878)-net in base 81, because

1 times m-reduction [i] would yield (33, 69, 1953878)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 484693 980208 124333 540668 526137 300528 199026 499847 385335 236986 470460 565258 563353 569602 374630 138318 080393 572760 121897 183582 660318 179521 > 81⁶⁹ [i]