MinT - Best Known (68−38, 68, s)-Nets in Base 81

Best Known (68−38, 68, s)-Nets in Base 81

(68−38, 68, 370)-Net over F₈₁ — Constructive and digital

Digital (30, 68, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 68, 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]

(68−38, 68, 608)-Net over F₈₁ — Digital

Digital (30, 68, 608)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(68−38, 68, 670636)-Net in Base 81 — Upper bound on s

There is no (30, 68, 670637)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 5983 998657 201410 366567 938961 489872 919560 998338 520242 065731 843450 973564 466018 972570 304129 218691 668282 095690 113577 345642 938580 923441 > 81⁶⁸ [i]