MinT - Best Known (20, 20+41, s)-Nets in Base 81

Best Known (20, 20+41, s)-Nets in Base 81

(20, 20+41, 370)-Net over F₈₁ — Constructive and digital

Digital (20, 61, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 61, 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+41, 55156)-Net in Base 81 — Upper bound on s

There is no (20, 61, 55157)-net in base 81, because

1 times m-reduction [i] would yield (20, 60, 55157)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 3 230152 728327 040527 546872 589798 307337 242803 121211 817659 980991 952546 898983 596483 493591 662079 822397 672234 844685 819201 > 81⁶⁰ [i]