MinT - Best Known (243−113, 243, s)-Nets in Base 4

Best Known (243−113, 243, s)-Nets in Base 4

(243−113, 243, 130)-Net over F₄ — Constructive and digital

Digital (130, 243, 130)-net over F₄, using

t-expansion [i] based on digital (105, 243, 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]

(243−113, 243, 215)-Net over F₄ — Digital

Digital (130, 243, 215)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−113, 243, 2846)-Net in Base 4 — Upper bound on s

There is no (130, 243, 2847)-net in base 4, because

1 times m-reduction [i] would yield (130, 242, 2847)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 50 290579 881215 700327 190870 649507 268738 223662 122042 402391 893548 797042 048087 945631 015873 606968 808043 986533 817337 408531 086564 439508 180429 618098 303560 > 4²⁴² [i]