MinT - Best Known (77, 77+160, s)-Nets in Base 4

Best Known (77, 77+160, s)-Nets in Base 4

(77, 77+160, 104)-Net over F₄ — Constructive and digital

Digital (77, 237, 104)-net over F₄, using

t-expansion [i] based on digital (73, 237, 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+160, 112)-Net over F₄ — Digital

Digital (77, 237, 112)-net over F₄, using

t-expansion [i] based on digital (73, 237, 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+160, 556)-Net in Base 4 — Upper bound on s

There is no (77, 237, 557)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 55067 196323 833386 727768 757739 201415 415528 644510 734655 751742 675422 077170 632245 646101 642810 137413 084920 976600 051238 013694 386740 207057 210413 379760 > 4²³⁷ [i]