MinT - Best Known (260−166, 260, s)-Nets in Base 4

Best Known (260−166, 260, s)-Nets in Base 4

(260−166, 260, 104)-Net over F₄ — Constructive and digital

Digital (94, 260, 104)-net over F₄, using

t-expansion [i] based on digital (73, 260, 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]

(260−166, 260, 144)-Net over F₄ — Digital

Digital (94, 260, 144)-net over F₄, using

t-expansion [i] based on digital (91, 260, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(260−166, 260, 746)-Net in Base 4 — Upper bound on s

There is no (94, 260, 747)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 688501 728122 286692 618171 789802 265772 092113 815659 864490 029805 175755 536178 114808 132649 160346 508065 848824 244029 339859 467330 072049 152953 368028 064653 141166 023208 > 4²⁶⁰ [i]