MinT - Best Known (258−121, 258, s)-Nets in Base 4

Best Known (258−121, 258, s)-Nets in Base 4

(258−121, 258, 130)-Net over F₄ — Constructive and digital

Digital (137, 258, 130)-net over F₄, using

t-expansion [i] based on digital (105, 258, 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]

(258−121, 258, 221)-Net over F₄ — Digital

Digital (137, 258, 221)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(258−121, 258, 2881)-Net in Base 4 — Upper bound on s

There is no (137, 258, 2882)-net in base 4, because

1 times m-reduction [i] would yield (137, 257, 2882)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53663 583428 444166 194093 250532 692723 013328 199064 867277 545839 648266 557548 208080 830464 990458 810098 446098 679081 667526 637888 367775 134328 745024 574365 565873 113840 > 4²⁵⁷ [i]