MinT - Best Known (89−51, 89, s)-Nets in Base 64

Best Known (89−51, 89, s)-Nets in Base 64

(89−51, 89, 513)-Net over F₆₄ — Constructive and digital

Digital (38, 89, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 89, 513)-net over F₆₄, using
- net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]

(89−51, 89, 540)-Net over F₆₄ — Digital

Digital (38, 89, 540)-net over F₆₄, using

t-expansion [i] based on digital (37, 89, 540)-net over F₆₄, using
- net from sequence [i] based on digital (37, 539)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 37 and N(F) ≥ 540, using
    - a curve from the manYPoints database [i]

(89−51, 89, 368149)-Net in Base 64 — Upper bound on s

There is no (38, 89, 368150)-net in base 64, because

1 times m-reduction [i] would yield (38, 88, 368150)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 878 726598 471888 152952 437615 577403 039697 057280 459243 851702 832123 713909 257271 590849 846116 029335 644523 502877 427953 408045 237634 360108 500324 941453 474831 389651 121344 > 64⁸⁸ [i]