MinT - Best Known (242−113, 242, s)-Nets in Base 4

Best Known (242−113, 242, s)-Nets in Base 4

(242−113, 242, 130)-Net over F₄ — Constructive and digital

Digital (129, 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]

(242−113, 242, 211)-Net over F₄ — Digital

Digital (129, 242, 211)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−113, 242, 2775)-Net in Base 4 — Upper bound on s

There is no (129, 242, 2776)-net in base 4, because

1 times m-reduction [i] would yield (129, 241, 2776)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 504980 139111 054711 794912 918885 175925 822601 563745 573419 186543 817597 169356 600802 204703 505192 063475 263760 058253 894886 213177 245593 216157 852907 217480 > 4²⁴¹ [i]