MinT - Best Known (241−123, 241, s)-Nets in Base 4

Best Known (241−123, 241, s)-Nets in Base 4

(241−123, 241, 130)-Net over F₄ — Constructive and digital

Digital (118, 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]

(241−123, 241, 168)-Net over F₄ — Digital

Digital (118, 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]

(241−123, 241, 1786)-Net in Base 4 — Upper bound on s

There is no (118, 241, 1787)-net in base 4, because

1 times m-reduction [i] would yield (118, 240, 1787)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 212667 176374 980879 195716 835627 171204 332212 175497 761070 227439 876213 875307 007409 611847 807587 838859 655245 708632 947042 814203 340752 277911 568983 303200 > 4²⁴⁰ [i]