MinT - Best Known (20, 20+48, s)-Nets in Base 81

Best Known (20, 20+48, s)-Nets in Base 81

(20, 20+48, 370)-Net over F₈₁ — Constructive and digital

Digital (20, 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]

(20, 20+48, 31295)-Net in Base 81 — Upper bound on s

There is no (20, 68, 31296)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 5985 699980 326922 891102 752914 545524 895564 941188 395940 066005 201948 335576 799525 505874 155184 068569 074408 759921 120919 889953 136959 774721 > 81⁶⁸ [i]