MinT - Best Known (217−113, 217, s)-Nets in Base 4

Best Known (217−113, 217, s)-Nets in Base 4

(217−113, 217, 104)-Net over F₄ — Constructive and digital

Digital (104, 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]

(217−113, 217, 144)-Net over F₄ — Digital

Digital (104, 217, 144)-net over F₄, using

t-expansion [i] based on digital (91, 217, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(217−113, 217, 1474)-Net in Base 4 — Upper bound on s

There is no (104, 217, 1475)-net in base 4, because

1 times m-reduction [i] would yield (104, 216, 1475)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11491 829054 596888 773158 808330 032974 636480 065295 112969 179497 000213 855553 857065 878527 143970 202583 296617 623911 122569 457815 047310 111560 > 4²¹⁶ [i]