MinT - Best Known (89−55, 89, s)-Nets in Base 64

Best Known (89−55, 89, s)-Nets in Base 64

(89−55, 89, 513)-Net over F₆₄ — Constructive and digital

Digital (34, 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]

(89−55, 89, 133607)-Net in Base 64 — Upper bound on s

There is no (34, 89, 133608)-net in base 64, because

1 times m-reduction [i] would yield (34, 88, 133608)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 878 753374 781975 070101 856019 523556 216649 548944 129398 180554 486821 585581 373907 047717 727686 629290 040348 071313 041187 957312 688654 963287 851603 045377 436993 975118 180588 > 64⁸⁸ [i]