MinT - Best Known (230−122, 230, s)-Nets in Base 4

Best Known (230−122, 230, s)-Nets in Base 4

(230−122, 230, 130)-Net over F₄ — Constructive and digital

Digital (108, 230, 130)-net over F₄, using

t-expansion [i] based on digital (105, 230, 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]

(230−122, 230, 144)-Net over F₄ — Digital

Digital (108, 230, 144)-net over F₄, using

t-expansion [i] based on digital (91, 230, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(230−122, 230, 1413)-Net in Base 4 — Upper bound on s

There is no (108, 230, 1414)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 098669 061658 845323 851701 013838 344628 045360 335221 385198 946544 348704 345410 939058 560745 647100 697151 569669 883886 172614 587558 635464 916861 342640 > 4²³⁰ [i]