MinT - Best Known (242−121, 242, s)-Nets in Base 4

Best Known (242−121, 242, s)-Nets in Base 4

(242−121, 242, 130)-Net over F₄ — Constructive and digital

Digital (121, 242, 130)-net over F₄, using

t-expansion [i] based on digital (105, 242, 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]

(242−121, 242, 170)-Net over F₄ — Digital

Digital (121, 242, 170)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−121, 242, 1976)-Net in Base 4 — Upper bound on s

There is no (121, 242, 1977)-net in base 4, because

1 times m-reduction [i] would yield (121, 241, 1977)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 765254 130210 089883 107929 705717 345293 796327 040115 625770 129508 385605 590498 151494 548840 184276 501968 824749 826017 743742 150824 927105 183058 883658 442976 > 4²⁴¹ [i]