MinT - Best Known (80, 221, s)-Nets in Base 4

Best Known (80, 221, s)-Nets in Base 4

(80, 221, 104)-Net over F₄ — Constructive and digital

Digital (80, 221, 104)-net over F₄, using

t-expansion [i] based on digital (73, 221, 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]

(80, 221, 112)-Net over F₄ — Digital

Digital (80, 221, 112)-net over F₄, using

t-expansion [i] based on digital (73, 221, 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]

(80, 221, 643)-Net in Base 4 — Upper bound on s

There is no (80, 221, 644)-net in base 4, because

1 times m-reduction [i] would yield (80, 220, 644)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 024470 997060 077547 293323 235358 455059 028133 840802 695999 646320 382461 600133 432846 547373 388880 559010 334895 466564 511481 926797 687567 945504 > 4²²⁰ [i]