MinT - Best Known (108, 108+69, s)-Nets in Base 4

Best Known (108, 108+69, s)-Nets in Base 4

(108, 108+69, 130)-Net over F₄ — Constructive and digital

Digital (108, 177, 130)-net over F₄, using

t-expansion [i] based on digital (105, 177, 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, 108+69, 287)-Net over F₄ — Digital

Digital (108, 177, 287)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+69, 5872)-Net in Base 4 — Upper bound on s

There is no (108, 177, 5873)-net in base 4, because

1 times m-reduction [i] would yield (108, 176, 5873)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9180 917243 026480 500899 074529 837557 188470 722653 228229 214919 167717 456761 539847 476663 663722 749371 957331 727176 > 4¹⁷⁶ [i]