MinT - Best Known (258−144, 258, s)-Nets in Base 4

Best Known (258−144, 258, s)-Nets in Base 4

(258−144, 258, 130)-Net over F₄ — Constructive and digital

Digital (114, 258, 130)-net over F₄, using

t-expansion [i] based on digital (105, 258, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(258−144, 258, 165)-Net over F₄ — Digital

Digital (114, 258, 165)-net over F₄, using

t-expansion [i] based on digital (109, 258, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(258−144, 258, 1265)-Net in Base 4 — Upper bound on s

There is no (114, 258, 1266)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 225712 832710 307207 885297 117258 913436 624054 598595 801713 373182 775925 100537 076178 568870 193876 400859 998831 399852 456126 595603 202959 730086 318555 750092 266465 285994 > 4²⁵⁸ [i]