MinT - Best Known (74−41, 74, s)-Nets in Base 81

Best Known (74−41, 74, s)-Nets in Base 81

(74−41, 74, 370)-Net over F₈₁ — Constructive and digital

Digital (33, 74, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 74, 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]

(74−41, 74, 689)-Net over F₈₁ — Digital

Digital (33, 74, 689)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(74−41, 74, 959803)-Net in Base 81 — Upper bound on s

There is no (33, 74, 959804)-net in base 81, because

1 times m-reduction [i] would yield (33, 73, 959804)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 20 864811 572940 374488 955117 183580 978032 296546 344266 501259 879150 382459 267088 498286 039269 187944 364891 820950 794886 422554 088762 147208 045970 246401 > 81⁷³ [i]