MinT - Best Known (255−121, 255, s)-Nets in Base 4

Best Known (255−121, 255, s)-Nets in Base 4

(255−121, 255, 130)-Net over F₄ — Constructive and digital

Digital (134, 255, 130)-net over F₄, using

t-expansion [i] based on digital (105, 255, 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]

(255−121, 255, 210)-Net over F₄ — Digital

Digital (134, 255, 210)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(255−121, 255, 2685)-Net in Base 4 — Upper bound on s

There is no (134, 255, 2686)-net in base 4, because

1 times m-reduction [i] would yield (134, 254, 2686)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 843 476757 126943 188434 019178 525776 189336 692636 269087 776312 586094 037724 230023 117570 408454 271544 213065 977271 438769 367636 282595 919386 929445 365388 036642 296439 > 4²⁵⁴ [i]