MinT - Best Known (177−103, 177, s)-Nets in Base 4

Best Known (177−103, 177, s)-Nets in Base 4

(177−103, 177, 104)-Net over F₄ — Constructive and digital

Digital (74, 177, 104)-net over F₄, using

t-expansion [i] based on digital (73, 177, 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]

(177−103, 177, 112)-Net over F₄ — Digital

Digital (74, 177, 112)-net over F₄, using

t-expansion [i] based on digital (73, 177, 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]

(177−103, 177, 750)-Net in Base 4 — Upper bound on s

There is no (74, 177, 751)-net in base 4, because

1 times m-reduction [i] would yield (74, 176, 751)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9600 935624 762550 138221 491267 405931 149365 607585 940941 765072 246865 862046 632774 360267 925926 716237 782074 230944 > 4¹⁷⁶ [i]