MinT - Best Known (78, 199, s)-Nets in Base 4

Best Known (78, 199, s)-Nets in Base 4

(78, 199, 104)-Net over F₄ — Constructive and digital

Digital (78, 199, 104)-net over F₄, using

t-expansion [i] based on digital (73, 199, 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]

(78, 199, 112)-Net over F₄ — Digital

Digital (78, 199, 112)-net over F₄, using

t-expansion [i] based on digital (73, 199, 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]

(78, 199, 701)-Net in Base 4 — Upper bound on s

There is no (78, 199, 702)-net in base 4, because

1 times m-reduction [i] would yield (78, 198, 702)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 166337 178532 468900 497473 746291 447117 264756 012214 350612 077905 055707 252433 039225 522643 739533 195084 740745 121517 806858 165425 > 4¹⁹⁸ [i]