MinT - Best Known (108, 240, s)-Nets in Base 4

Best Known (108, 240, s)-Nets in Base 4

(108, 240, 130)-Net over F₄ — Constructive and digital

Digital (108, 240, 130)-net over F₄, using

t-expansion [i] based on digital (105, 240, 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]

(108, 240, 144)-Net over F₄ — Digital

Digital (108, 240, 144)-net over F₄, using

t-expansion [i] based on digital (91, 240, 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]

(108, 240, 1256)-Net in Base 4 — Upper bound on s

There is no (108, 240, 1257)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 223456 754282 518798 190865 165583 528086 143097 647936 600036 206453 149510 775408 072807 444681 991205 441116 127173 486832 066092 345398 598964 672985 603289 948476 > 4²⁴⁰ [i]