MinT - Best Known (76, 76+153, s)-Nets in Base 4

Best Known (76, 76+153, s)-Nets in Base 4

(76, 76+153, 104)-Net over F₄ — Constructive and digital

Digital (76, 229, 104)-net over F₄, using

t-expansion [i] based on digital (73, 229, 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]

(76, 76+153, 112)-Net over F₄ — Digital

Digital (76, 229, 112)-net over F₄, using

t-expansion [i] based on digital (73, 229, 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]

(76, 76+153, 560)-Net in Base 4 — Upper bound on s

There is no (76, 229, 561)-net in base 4, because

1 times m-reduction [i] would yield (76, 228, 561)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 194522 520018 567347 216918 163309 777562 404751 857381 205308 666396 996908 472411 742897 215737 111617 257384 190024 361947 297681 839680 784965 046889 002400 > 4²²⁸ [i]