MinT - Best Known (244−121, 244, s)-Nets in Base 4

Best Known (244−121, 244, s)-Nets in Base 4

(244−121, 244, 130)-Net over F₄ — Constructive and digital

Digital (123, 244, 130)-net over F₄, using

t-expansion [i] based on digital (105, 244, 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]

(244−121, 244, 176)-Net over F₄ — Digital

Digital (123, 244, 176)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−121, 244, 2072)-Net in Base 4 — Upper bound on s

There is no (123, 244, 2073)-net in base 4, because

1 times m-reduction [i] would yield (123, 243, 2073)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 205 404856 163764 214020 794129 343378 285237 418558 804685 216406 758726 151463 468886 798047 531906 339301 959473 330076 219246 117131 537031 326437 454963 369029 303808 > 4²⁴³ [i]