MinT - Best Known (127, 127+95, s)-Nets in Base 4

Best Known (127, 127+95, s)-Nets in Base 4

(127, 127+95, 130)-Net over F₄ — Constructive and digital

Digital (127, 222, 130)-net over F₄, using

t-expansion [i] based on digital (105, 222, 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+95, 258)-Net over F₄ — Digital

Digital (127, 222, 258)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+95, 4110)-Net in Base 4 — Upper bound on s

There is no (127, 222, 4111)-net in base 4, because

1 times m-reduction [i] would yield (127, 221, 4111)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 428183 402054 450400 321372 807741 973371 880329 206487 483965 243705 849111 508496 839699 616799 080833 494493 688387 032045 393922 471368 318745 627136 > 4²²¹ [i]