MinT - Best Known (228−109, 228, s)-Nets in Base 4

Best Known (228−109, 228, s)-Nets in Base 4

(228−109, 228, 130)-Net over F₄ — Constructive and digital

Digital (119, 228, 130)-net over F₄, using

t-expansion [i] based on digital (105, 228, 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]

(228−109, 228, 186)-Net over F₄ — Digital

Digital (119, 228, 186)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−109, 228, 2328)-Net in Base 4 — Upper bound on s

There is no (119, 228, 2329)-net in base 4, because

1 times m-reduction [i] would yield (119, 227, 2329)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46679 507610 235473 000306 348251 250142 172112 116704 736954 188237 635342 858125 601594 208327 951963 118102 198469 550343 639115 241753 239108 572014 679200 > 4²²⁷ [i]