MinT - Best Known (90−48, 90, s)-Nets in Base 64

Best Known (90−48, 90, s)-Nets in Base 64

(90−48, 90, 513)-Net over F₆₄ — Constructive and digital

Digital (42, 90, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 90, 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]

(90−48, 90, 862)-Net over F₆₄ — Digital

Digital (42, 90, 862)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−48, 90, 922978)-Net in Base 64 — Upper bound on s

There is no (42, 90, 922979)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3 599194 883289 643189 126911 136870 057343 548277 374650 516200 981086 722707 521418 640182 576955 786099 117418 537114 527816 121005 496285 841745 908527 841693 810166 075243 533516 117044 > 64⁹⁰ [i]