MinT - Best Known (127, 127+117, s)-Nets in Base 4

Best Known (127, 127+117, s)-Nets in Base 4

(127, 127+117, 130)-Net over F₄ — Constructive and digital

Digital (127, 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]

(127, 127+117, 196)-Net over F₄ — Digital

Digital (127, 244, 196)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+117, 2444)-Net in Base 4 — Upper bound on s

There is no (127, 244, 2445)-net in base 4, because

1 times m-reduction [i] would yield (127, 243, 2445)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 202 562536 249076 455508 745672 849965 693472 596057 852062 258814 282280 484838 319327 294555 768109 888350 070448 792884 116933 671401 331126 156765 365837 210423 279504 > 4²⁴³ [i]