MinT - Best Known (29, 68, s)-Nets in Base 81

Best Known (29, 68, s)-Nets in Base 81

(29, 68, 370)-Net over F₈₁ — Constructive and digital

Digital (29, 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]

(29, 68, 508)-Net over F₈₁ — Digital

Digital (29, 68, 508)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(29, 68, 532155)-Net in Base 81 — Upper bound on s

There is no (29, 68, 532156)-net in base 81, because

1 times m-reduction [i] would yield (29, 67, 532156)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 73 875199 361959 777622 697378 626226 487262 289184 975973 623075 463988 535182 378136 477012 696783 859394 499019 063684 728142 705307 204902 227521 > 81⁶⁷ [i]