MinT - Best Known (127, 127+115, s)-Nets in Base 4

Best Known (127, 127+115, s)-Nets in Base 4

(127, 127+115, 130)-Net over F₄ — Constructive and digital

Digital (127, 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]

(127, 127+115, 200)-Net over F₄ — Digital

Digital (127, 242, 200)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+115, 2538)-Net in Base 4 — Upper bound on s

There is no (127, 242, 2539)-net in base 4, because

1 times m-reduction [i] would yield (127, 241, 2539)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 732005 027888 499338 711563 362093 422757 661966 505351 631594 750238 658502 792296 221442 837482 822912 455959 432353 716070 157791 901482 979833 644708 600922 096600 > 4²⁴¹ [i]