MinT - Best Known (127, 127+109, s)-Nets in Base 4

Best Known (127, 127+109, s)-Nets in Base 4

(127, 127+109, 130)-Net over F₄ — Constructive and digital

Digital (127, 236, 130)-net over F₄, using

t-expansion [i] based on digital (105, 236, 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+109, 214)-Net over F₄ — Digital

Digital (127, 236, 214)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+109, 2869)-Net in Base 4 — Upper bound on s

There is no (127, 236, 2870)-net in base 4, because

1 times m-reduction [i] would yield (127, 235, 2870)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3059 247197 171898 548421 778775 832457 890042 948582 720544 579872 165807 910425 532108 713826 253768 481360 033184 652769 174273 234082 921452 847472 967023 887096 > 4²³⁵ [i]