MinT - Best Known (36, 36+87, s)-Nets in Base 9

Best Known (36, 36+87, s)-Nets in Base 9

(36, 36+87, 81)-Net over F₉ — Constructive and digital

Digital (36, 123, 81)-net over F₉, using

t-expansion [i] based on digital (32, 123, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(36, 36+87, 128)-Net over F₉ — Digital

Digital (36, 123, 128)-net over F₉, using

t-expansion [i] based on digital (33, 123, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(36, 36+87, 1049)-Net in Base 9 — Upper bound on s

There is no (36, 123, 1050)-net in base 9, because

1 times m-reduction [i] would yield (36, 122, 1050)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 264 789454 762414 860956 577956 394944 455625 490833 621268 442112 574716 187807 035764 329575 252669 754379 067399 296772 092654 969137 > 9¹²² [i]