MinT - Best Known (241−115, 241, s)-Nets in Base 4

Best Known (241−115, 241, s)-Nets in Base 4

(241−115, 241, 130)-Net over F₄ — Constructive and digital

Digital (126, 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]

(241−115, 241, 196)-Net over F₄ — Digital

Digital (126, 241, 196)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−115, 241, 2476)-Net in Base 4 — Upper bound on s

There is no (126, 241, 2477)-net in base 4, because

1 times m-reduction [i] would yield (126, 240, 2477)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 191617 565939 483121 482048 545491 258557 914749 279618 602088 995499 008012 817097 732658 984774 728550 284930 186015 619682 946970 773203 498488 461969 192665 260800 > 4²⁴⁰ [i]