MinT - Best Known (125, 242, s)-Nets in Base 4

Best Known (125, 242, s)-Nets in Base 4

(125, 242, 130)-Net over F₄ — Constructive and digital

Digital (125, 242, 130)-net over F₄, using

t-expansion [i] based on digital (105, 242, 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]

(125, 242, 189)-Net over F₄ — Digital

Digital (125, 242, 189)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(125, 242, 2328)-Net in Base 4 — Upper bound on s

There is no (125, 242, 2329)-net in base 4, because

1 times m-reduction [i] would yield (125, 241, 2329)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 762277 559691 087398 548408 831766 909059 466279 265464 985408 146105 073772 038102 329800 224986 738555 039242 011377 388869 686257 928161 359112 362697 309537 506560 > 4²⁴¹ [i]