MinT - Best Known (48−26, 48, s)-Nets in Base 81

Best Known (48−26, 48, s)-Nets in Base 81

(48−26, 48, 370)-Net over F₈₁ — Constructive and digital

Digital (22, 48, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 48, 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]

(48−26, 48, 600)-Net over F₈₁ — Digital

Digital (22, 48, 600)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(48−26, 48, 788908)-Net in Base 81 — Upper bound on s

There is no (22, 48, 788909)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 40 484003 512233 880959 306143 611589 266443 878048 170231 451387 744497 459904 418911 120667 005745 969361 > 81⁴⁸ [i]