MinT - Best Known (31, 31+35, s)-Nets in Base 81

Best Known (31, 31+35, s)-Nets in Base 81

(31, 31+35, 370)-Net over F₈₁ — Constructive and digital

Digital (31, 66, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 66, 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]

(31, 31+35, 874)-Net over F₈₁ — Digital

Digital (31, 66, 874)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(31, 31+35, 1778286)-Net in Base 81 — Upper bound on s

There is no (31, 66, 1778287)-net in base 81, because

1 times m-reduction [i] would yield (31, 65, 1778287)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 11259 701350 698021 631631 473927 086280 662471 652750 316284 078404 496799 316378 414763 102839 968972 739636 423968 320092 404262 775603 801521 > 81⁶⁵ [i]