MinT - Best Known (241−117, 241, s)-Nets in Base 4

Best Known (241−117, 241, s)-Nets in Base 4

(241−117, 241, 130)-Net over F₄ — Constructive and digital

Digital (124, 241, 130)-net over F₄, using

t-expansion [i] based on digital (105, 241, 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]

(241−117, 241, 186)-Net over F₄ — Digital

Digital (124, 241, 186)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−117, 241, 2272)-Net in Base 4 — Upper bound on s

There is no (124, 241, 2273)-net in base 4, because

1 times m-reduction [i] would yield (124, 240, 2273)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 200100 983407 170096 126718 534229 347722 946064 209345 267980 449357 459325 668288 107180 946286 265726 070040 505695 607146 862143 449857 430814 518096 947971 707680 > 4²⁴⁰ [i]