MinT - Best Known (77, 77+176, s)-Nets in Base 4

Best Known (77, 77+176, s)-Nets in Base 4

(77, 77+176, 104)-Net over F₄ — Constructive and digital

Digital (77, 253, 104)-net over F₄, using

t-expansion [i] based on digital (73, 253, 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]

(77, 77+176, 112)-Net over F₄ — Digital

Digital (77, 253, 112)-net over F₄, using

t-expansion [i] based on digital (73, 253, 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]

(77, 77+176, 532)-Net in Base 4 — Upper bound on s

There is no (77, 253, 533)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 232 129691 445525 096012 173527 381181 009076 116352 795628 593250 796269 622007 408409 578871 023779 085743 540630 061734 324762 077486 072824 504969 001081 681759 137939 087040 > 4²⁵³ [i]