MinT - Best Known (75, 217, s)-Nets in Base 4

Best Known (75, 217, s)-Nets in Base 4

(75, 217, 104)-Net over F₄ — Constructive and digital

Digital (75, 217, 104)-net over F₄, using

t-expansion [i] based on digital (73, 217, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(75, 217, 112)-Net over F₄ — Digital

Digital (75, 217, 112)-net over F₄, using

t-expansion [i] based on digital (73, 217, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(75, 217, 572)-Net in Base 4 — Upper bound on s

There is no (75, 217, 573)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48230 641842 567836 353742 906973 058565 523080 856346 455451 005726 031860 802318 571394 445088 181882 539711 018453 865274 567800 231163 290095 110720 > 4²¹⁷ [i]