MinT - Best Known (258−140, 258, s)-Nets in Base 4

Best Known (258−140, 258, s)-Nets in Base 4

(258−140, 258, 130)-Net over F₄ — Constructive and digital

Digital (118, 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]

(258−140, 258, 168)-Net over F₄ — Digital

Digital (118, 258, 168)-net over F₄, using

t-expansion [i] based on digital (115, 258, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(258−140, 258, 1427)-Net in Base 4 — Upper bound on s

There is no (118, 258, 1428)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 219152 480162 065765 689821 117997 660588 718345 347791 969110 617866 734677 293246 491659 417768 217064 897851 695793 360976 340238 321816 598497 843763 607549 693382 720624 136248 > 4²⁵⁸ [i]