MinT - Best Known (108, 108+89, s)-Nets in Base 4

Best Known (108, 108+89, s)-Nets in Base 4

(108, 108+89, 130)-Net over F₄ — Constructive and digital

Digital (108, 197, 130)-net over F₄, using

t-expansion [i] based on digital (105, 197, 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+89, 195)-Net over F₄ — Digital

Digital (108, 197, 195)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+89, 2729)-Net in Base 4 — Upper bound on s

There is no (108, 197, 2730)-net in base 4, because

1 times m-reduction [i] would yield (108, 196, 2730)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10236 235239 866763 876031 266391 180259 176650 135533 623743 302697 028363 499698 626873 047590 820552 737028 481670 252405 359144 290464 > 4¹⁹⁶ [i]