MinT - Best Known (223−101, 223, s)-Nets in Base 4

Best Known (223−101, 223, s)-Nets in Base 4

(223−101, 223, 130)-Net over F₄ — Constructive and digital

Digital (122, 223, 130)-net over F₄, using

t-expansion [i] based on digital (105, 223, 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]

(223−101, 223, 216)-Net over F₄ — Digital

Digital (122, 223, 216)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−101, 223, 3018)-Net in Base 4 — Upper bound on s

There is no (122, 223, 3019)-net in base 4, because

1 times m-reduction [i] would yield (122, 222, 3019)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45 577308 658580 495484 478429 009789 240660 475374 614138 027393 149090 894683 827997 618732 030887 511839 572879 077679 039384 756344 612209 484433 156476 > 4²²² [i]