MinT - Best Known (259−152, 259, s)-Nets in Base 4

Best Known (259−152, 259, s)-Nets in Base 4

(259−152, 259, 130)-Net over F₄ — Constructive and digital

Digital (107, 259, 130)-net over F₄, using

t-expansion [i] based on digital (105, 259, 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]

(259−152, 259, 144)-Net over F₄ — Digital

Digital (107, 259, 144)-net over F₄, using

t-expansion [i] based on digital (91, 259, 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]

(259−152, 259, 1031)-Net in Base 4 — Upper bound on s

There is no (107, 259, 1032)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 862785 331685 344597 349089 974595 767333 824627 421372 980351 374022 847660 510993 510298 058891 213645 547436 137771 591810 213673 224077 148050 763117 942509 864126 486465 547136 > 4²⁵⁹ [i]