MinT - Best Known (260−152, 260, s)-Nets in Base 4

Best Known (260−152, 260, s)-Nets in Base 4

(260−152, 260, 130)-Net over F₄ — Constructive and digital

Digital (108, 260, 130)-net over F₄, using

t-expansion [i] based on digital (105, 260, 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]

(260−152, 260, 144)-Net over F₄ — Digital

Digital (108, 260, 144)-net over F₄, using

t-expansion [i] based on digital (91, 260, 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]

(260−152, 260, 1052)-Net in Base 4 — Upper bound on s

There is no (108, 260, 1053)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 668496 986078 113570 084759 701643 029829 593183 598010 612913 376364 350489 842523 112656 652604 591741 106741 443344 169259 200514 796112 604116 185431 326756 386426 673136 589200 > 4²⁶⁰ [i]