MinT - Best Known (88−74, 88, s)-Nets in Base 64

Best Known (88−74, 88, s)-Nets in Base 64

(88−74, 88, 177)-Net over F₆₄ — Constructive and digital

Digital (14, 88, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 88, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(88−74, 88, 257)-Net over F₆₄ — Digital

Digital (14, 88, 257)-net over F₆₄, using

t-expansion [i] based on digital (12, 88, 257)-net over F₆₄, using
- net from sequence [i] based on digital (12, 256)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 12 and N(F) ≥ 257, using
    - K_1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]

(88−74, 88, 4577)-Net in Base 64 — Upper bound on s

There is no (14, 88, 4578)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 884 964683 181087 880088 453967 485484 185474 009940 609937 830097 755212 094617 929223 752637 701808 374908 373641 051779 229662 468792 785001 067361 528428 221760 581410 375204 434064 > 64⁸⁸ [i]