MinT - Best Known (89−48, 89, s)-Nets in Base 64

Best Known (89−48, 89, s)-Nets in Base 64

(89−48, 89, 513)-Net over F₆₄ — Constructive and digital

Digital (41, 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]

(89−48, 89, 791)-Net over F₆₄ — Digital

Digital (41, 89, 791)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−48, 89, 776127)-Net in Base 64 — Upper bound on s

There is no (41, 89, 776128)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 56237 694528 663470 752811 315725 101614 091679 281733 456613 587797 422222 804557 672251 902430 107031 868394 497322 932422 768857 884562 715487 765023 178180 764310 467957 470664 719221 > 64⁸⁹ [i]