MinT - Best Known (258−156, 258, s)-Nets in Base 4

Best Known (258−156, 258, s)-Nets in Base 4

(258−156, 258, 104)-Net over F₄ — Constructive and digital

Digital (102, 258, 104)-net over F₄, using

t-expansion [i] based on digital (73, 258, 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]

(258−156, 258, 144)-Net over F₄ — Digital

Digital (102, 258, 144)-net over F₄, using

t-expansion [i] based on digital (91, 258, 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]

(258−156, 258, 912)-Net in Base 4 — Upper bound on s

There is no (102, 258, 913)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 216793 153152 226765 261744 271587 293853 609829 055811 153109 179626 973696 454152 729899 380992 401611 461021 674606 765706 641604 139290 420848 634858 840532 564626 028388 274480 > 4²⁵⁸ [i]