MinT - Best Known (78, 78+90, s)-Nets in Base 4

Best Known (78, 78+90, s)-Nets in Base 4

(78, 78+90, 104)-Net over F₄ — Constructive and digital

Digital (78, 168, 104)-net over F₄, using

t-expansion [i] based on digital (73, 168, 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, 78+90, 112)-Net over F₄ — Digital

Digital (78, 168, 112)-net over F₄, using

t-expansion [i] based on digital (73, 168, 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, 78+90, 1002)-Net in Base 4 — Upper bound on s

There is no (78, 168, 1003)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 141202 001995 517847 172811 271741 505422 642224 208053 845075 579984 255535 974786 456061 608983 182156 244831 942304 > 4¹⁶⁸ [i]