MinT - Best Known (241−113, 241, s)-Nets in Base 4

Best Known (241−113, 241, s)-Nets in Base 4

(241−113, 241, 130)-Net over F₄ — Constructive and digital

Digital (128, 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]

(241−113, 241, 208)-Net over F₄ — Digital

Digital (128, 241, 208)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−113, 241, 2706)-Net in Base 4 — Upper bound on s

There is no (128, 241, 2707)-net in base 4, because

1 times m-reduction [i] would yield (128, 240, 2707)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 125716 879119 265196 147523 252891 265662 348902 532731 983914 492457 325205 381549 785611 684698 946742 544532 402073 104641 728334 439205 771195 550935 108926 760560 > 4²⁴⁰ [i]