MinT - Best Known (82−68, 82, s)-Nets in Base 64

Best Known (82−68, 82, s)-Nets in Base 64

(82−68, 82, 177)-Net over F₆₄ — Constructive and digital

Digital (14, 82, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 82, 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]

(82−68, 82, 257)-Net over F₆₄ — Digital

Digital (14, 82, 257)-net over F₆₄, using

t-expansion [i] based on digital (12, 82, 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]

(82−68, 82, 4860)-Net in Base 64 — Upper bound on s

There is no (14, 82, 4861)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 12815 035010 678165 931629 679013 546494 953623 575445 594969 544643 906774 721380 514340 279101 625854 799564 771576 045236 076926 809814 983546 390061 700933 771926 450570 > 64⁸² [i]