MinT - Best Known (241−121, 241, s)-Nets in Base 4

Best Known (241−121, 241, s)-Nets in Base 4

(241−121, 241, 130)-Net over F₄ — Constructive and digital

Digital (120, 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]

(241−121, 241, 168)-Net over F₄ — Digital

Digital (120, 241, 168)-net over F₄, using

t-expansion [i] based on digital (115, 241, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(241−121, 241, 1930)-Net in Base 4 — Upper bound on s

There is no (120, 241, 1931)-net in base 4, because

1 times m-reduction [i] would yield (120, 240, 1931)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 216990 703592 423180 016806 825806 107916 824613 593926 547784 594730 122200 108922 172845 000104 385083 127559 645738 623202 353790 803796 517615 635447 219464 950880 > 4²⁴⁰ [i]